FIG. 1(a) depicts a multipath channel through which television signals propagate from a transmitter 1 to a receiver 2. As depicted, the television signals arrive at the receiver 2 via a number of paths A, B, C, D including a short direct path A, and longer paths B, C, D in which the signals reflect off of features of the channel (e.g., buildings, mountains, and the ionosphere). All of these signals are superimposed at the receiver 2. The signals arriving via the paths B-D are weaker than the signal arriving via the direct path A. Thus, the signal arriving via the path A produces the strongest video image at the receiver 2 and is referred to as the "main" signal. Furthermore, the signals arriving via the paths B-D are delayed with respect to the main signal arriving via the path A. As a result, the signals arriving via the paths B-D produce delayed duplicate video images or "post-ghosts" of the main signal arriving via the path A as depicted in FIG. 1(b).
Another multipath channel is depicted in FIG. 1(c). As depicted, a signal arrives via a short path E through buildings 3. A signal also arrives via a longer reflection path F and is thus delayed with respect to the signal arriving via the short path E. In this case, it is assumed that the signal arriving via path E is attenuated to a greater extent (by virtue of propagating through the buildings 3) than the signal arriving via the path F. In such a case, the weaker signal arriving via the path E produces a "pre-ghost" of the main signal arriving via the path F as depicted in FIG. 1(d).
It is desirable to eliminate both pre-ghosts and post-ghosts of the main signal in order to improve reception. Several ghost cancelling systems have been proposed in the form of a channel equalizer. FIG. 2(a) depicts a transmission path including a transmitter 4, a multipath channel 5 and a receiver 6 which includes a channel equalizer 7 and a display device 8. In such systems, an ideal ghost cancelling reference (GCR) signal R.sub.ideal (t) is inserted into the video signal V(t), e.g., during the vertical blanking interval, prior to transmission from the transmitter 4. The transmitter 4 transmits the video signal V(t) (including the ideal GCR signal R.sub.ideal (t)) which propagates through the multipath channel 5 having an impulse response A(t). By virtue of propagating through the multipath channel 5, a signal with ghosts V(t)*A(t) (including R.sub.ideal (t)*A(t)) is produced, where "*" means "convolved with." This signal V(t)*A(t) is received at the receiver 6 where it is inputted to the channel equalizer 7. The channel equalizer 7 has an impulse response W(t) and therefore outputs the signal V(t)*A(t)*W(t). The channel equalizer 7 is designed so that V(t)*A(t)*W(t)=V(t). The signal outputted from the channel equalizer 7 is then displayed on a display device such as a cathode ray tube (CRT) screen 8.
The channel equalizer 7 is shown in greater detail in FIG 2(b). As depicted in FIG. 2(b), the channel equalizer 7 typically includes an analog to digital converter (ADC) 9 which converts the received video signal V(t)*A(t) to digital form. Illustratively, the received video signal V(t)*A(t) has an upper cutoff frequency of approximately 4.2 MHz. The received video signal V(t)*A(t) is illustratively sampled in the ADC 9 at 14.32 MHz. These samples are inputted to an extraction circuit 10 which extracts the received GCR signal R.sub.rec (t) (where R.sub.rec (t)=R.sub.ideal (t)*A(t)) from the received video signal V(t)*A(t). This received GCR signal R.sub.rec (t) may be temporarily stored in a RAM 11. The received GCR signal R.sub.rec (t) is then compared to an ideal GCR signal R.sub.ideal (t) (obtained from a circuit 12, such as a ROM) in a CPU or digital signal processor (DSP) 13. Based on the discrepancy between the received R.sub.rec (t) and the ideal R.sub.ideal (t) GCR signals, the CPU or DSP 13 generates filtering or tap coefficients for cancelling ghosts in the received video signal V(t)*A(t). The tap coefficients are transferred to a transversal filter 14. The received video signal V(t)*A(t) is accordingly digitally filtered by the transversal filter 14 using the tap coefficients determined by the CpU or DSp 13. The filtered video signal outputted by the transversal filter 14 may illustratively be converted back to analog form in a digital to analog converter (DAC) 15.
FIG. 2(c) shows an exemplary prior art transversal filter 14 including a finite impulse response filter (FIR) 16, and an infinite impulse response filter (IIR) 17. Illustratively, the IIR filter 17 is formed by connecting a second FIR filter 18 in negative a feedback path of an adder 19 to which the FIR filter 16 is connected. U.S. Pat. No. 4,953,026 discloses conventional circuits for implementing a FIR or IIR filter.
Several conventional algorithms have been proposed for obtaining FIR and IIR tap coefficients (see U.S. Pat. No. 4,947,252). Tap coefficients of the transversal filter 14 (FIG 2(c)) within the channel equalizer 7 (FIG. 2(a)) may be derived from the formula V(t)*A(t)*W(t)=V(t). According to one conventional method, called a division method, the tap coefficients are determined so that ##EQU1## where V(f), A(f) and W(f) are the video signal, the channel impulse response and the equalizer impulse response, in the frequency domain, respectively. The video signal V(f) and the channel impulse response A(f) are both unknown and vary over time. If, however, a known ghost cancelling reference (GCR) signal R.sub.ideal (t) is inserted into the video signal V(t) prior to transmission, then the tap coefficients may be generated by comparing the received and ideal GCR signals R.sub.rec (t) and R.sub.ideal (t) In such a case, the above formula may be simplified to: ##EQU2##
FIG. 3 depicts one conventional division method algorithm for obtaining tap coefficients. Typically, the FIR filter 16 utilizes a relatively small number of taps for cancelling "nearby" ghosts (e.g., a ghost separated by 2 .mu.sec from the main signal). To determine nearby ghost tap coefficients according to this method, the signal R.sub.rec (t) is first windowed over a short interval appropriate for cancelling nearby ghosts to produce the signal R.sub.rec '(t) in step 40 (herein, one prime mark indicates short term windowing). Next, in step 42, the signal R.sub.rec '(t) is fourier transformed to produce the signal R.sub.rec '(f) Then, in step 44, the nearby ghost tap coefficient signal W.sub.near (f) is determined by the formula ##EQU3##
As depicted in FIG. 4, W.sub.near (f) is plotted from zero to half the sampling frequency f.sub.s/2 (where f.sub.s is the sampling frequency, e.g., 14.32 MHz). As the signal is symmetric about f.sub.s/2, the discussion herein considers only the frequency band below f.sub.s/2. As depicted, W.sub.near (f) has a large noise component above the upper cutoff frequency f.sub.v of the received video signal V(t)*A(t) (e.g., 4.2 MHz). At certain frequencies, this noise component exceeds the value one (indicated by a dashed line). As such, the signal W.sub.near (f) is often subsequently compensated to zero above f.sub.v, i.e., above 4.2 MHz, in the frequency domain, by dividing the tap coefficient signal W.sub.near (f) by another signal. The signal W.sub.near (f) after compensation is depicted in FIG. 5. As depicted, the compensated signal W.sub.near (f) resembles the impulse response of a low pass filter.
Returning now to FIG. 3, in step 46, this signal W.sub.near (f) is converted to the time domain by computing its inverse fourier transform. Finally, in step 48, the signal W.sub.near (t) is windowed over a short interval (appropriate for producing nearby ghost tap coefficients) to produce the signal W.sub.near '(t).
The windowed nearby ghost tap coefficient signal W.sub.near '(t) is depicted in FIG. 6. As depicted, the signal W.sub.near '(t) has a main peak centered approximately at the time interval of a ghost. The signal W.sub.near '(t), however, is spread out over the time domain having other maxima and minima where no ghost exists.
The prior art division method of FIG. 3 also produces tap coefficients for the IIR filter 17. The IIR filter 17 typically has a large number of tap coefficients for cancelling "non-nearby" or "normal" ghosts (e.g., a ghost separated by 40 .mu.sec from the main signal).
In step 50, the received GCR signal R.sub.rec (t) is windowed appropriately for cancelling normal ghosts to produce the signal R.sub.rec ''(t) (herein, two prime marks means long term windowing). Next, in step 52, the signal R.sub.rec "(t) is fourier transformed to produce the signal R.sub.rec "(f). In step 54, the windowed nearby tap coefficient signal W.sub.near '(t) (obtained in step 48) is fourier transformed to produce the signal W.sub.near '(f). These two signals R.sub.rec "(f) and W.sub.near '(f) are used to form the signal h(f) in step 56. h(f) is determined by the formula: EQU h(f)=R.sub.ideal (f)-R.sub.rec "(f).multidot.W.sub.near '(f) (4)
Then in step 58, the normal ghost tap coefficient signal W.sub.norm (f) is determined by the formula: ##EQU4## In step 60, the inverse fourier transform of W.sub.norm (f) is computed to produce the signal W.sub.norm (t) Finally, W.sub.norm (t) is windowed over a long interval (appropriate for producing normal ghost tap coefficients) to produce the signal W.sub.norm "(t) in step 62.
This prior art division method for generating tap coefficients has disadvantages. When compensated to zero, the tap coefficient signal in the frequency domain W.sub.near (f) resembles the impulse response of a low pass filter. As such, when converted to the time domain, the tap coefficient signal W.sub.near '(t) spreads out over the time domain having minima and maxima where no ghosts are located. Because the tap coefficient signal W.sub.near '(t) is spread out over the time domain, a greater number of tap coefficients are required to filter adequately a video signal.
It is an object of the present invention to overcome the disadvantages of the prior art division method.